Difference between revisions of "005 Sample Final A, Question 22"

Revision as of 12:20, 20 May 2015

Question Consider the following sequence,

-3,1,-{\frac {1}{3}},{\frac {1}{9}},-{\frac {1}{27}},\cdots

a. Determine a formula for $a_{n}$ , the n-th term of the sequence.
b. Find the sum $\displaystyle {\sum _{k=1}^{\infty }a_{k}}$

Step 1:

Step 2:

Step 3:

Step 4:

Final Answer:

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1:
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
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+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 2:
 |-
-|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
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+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 3:
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
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 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
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+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 4:
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-|e) True.
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+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Step 5:
 |-
-|f) False.
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+|-
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+|-
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+|}
+{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+! Final Answer:
+|-
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 |}